Alex Furman : Introduction to the work of "7 samurais"

Posted by Alexander Furman , part of the Graduate Groups and Dynamics Seminar.

At

Jan. 23, 2019, 4 p.m.

In

612 SEO

Abstract

This semester we plan to discuss the recent work of Abert-Bergeron-Biringer-Gelander-Nikolov-Raimbault-Samet) and to (hereafter 7s) that, among other things, discusses the asymptotic growth of the Betti numbers of compact locally symmetric manifolds $b_i(M)/vol(M)$ as $vol(M)\to \infty$, where $M=\Gamma\backslash X$ are quotients of a fixed (higher rank) irreducible symmetric space. To understand these results (and to put them in perspective) we need to discuss a variety of important and cool math topics: - L^2-Betti numbers - Luck's Approximation Theorem - Benjaminy-Schramm convergence - Invariant Random Subgroups - Stuck-Zimmer theorem - and more... There is some topology, geometry, dynamics, and number theory in this all. In this first talk we will give a general overview, and discuss soem organizational topics.